Introduction to Computer Engineering by Richard E. Haskell Basic Digital Design Module M1.2 Section 3.2

Introduction to Computer Engineering by Richard E. Haskell Basic Digital Design Sum of Products Design –Minterms Product of Sums Design –Maxterms

Introduction to Computer Engineering by Richard E. Haskell Exclusive-OR Gate XOR X Y Z Z = X $ Y X Y Z

Introduction to Computer Engineering by Richard E. Haskell Sum of Products Design X Y minterms 0 0 m0 = !X & !Y 0 1 m1 = !X & Y 1 0 m2 = X & !Y 1 1 m3 = X & Y

Introduction to Computer Engineering by Richard E. Haskell Sum of Products Design X Y Z Design an XOR gate m1 = !X & Y m2 = X & !Y Z = m1 # m2 = (!X & Y) # (X & !Y)

Introduction to Computer Engineering by Richard E. Haskell Sum of Products: Exclusive-OR !X & Y X & !Y Z = (!X & Y) # (X & !Y)

Introduction to Computer Engineering by Richard E. Haskell Precedence of Logical Operators All ! operations are done first All & operations are done next All # operations are done last Z = (!X & Y) # (X & !Y) = !X & Y # X & !Y

Introduction to Computer Engineering by Richard E. Haskell Problem

Introduction to Computer Engineering by Richard E. Haskell Basic Digital Design Sum of Products Design –Minterms Product of Sums Design –Maxterms

Introduction to Computer Engineering by Richard E. Haskell Product of Sums Design Maxterms: A maxterm is NOT a minterm maxterm M0 = NOT minterm m0 M0 = !m0 = !(!X & !Y) = !!(!!X # !!Y) = X # Y

Introduction to Computer Engineering by Richard E. Haskell Product of Sums Design X Y minterms maxterms 0 0 m0 = !X & !Y M0 = !m0 = X # Y 0 1 m1 = !X & Y M1 = !m1 = X # !Y 1 0 m2 = X & !Y M2 = !m2 = !X # Y 1 1 m3 = X & Y M3 = !m3 = !X # !Y

Introduction to Computer Engineering by Richard E. Haskell Product of Sums Design X Y Z Design an XOR gate Z is NOT minterm m0 AND it is NOT minterm m3

Introduction to Computer Engineering by Richard E. Haskell Product of Sums Design X Y Z Design an XOR gate M0 = X # Y M3 = !X # !Y Z = M0 & M3 = (X # Y) & (!X # !Y)

Introduction to Computer Engineering by Richard E. Haskell Product of Sums: Exclusive-OR